Abstract: A new nodal method for directly solving the two-group neutron diffusion equation in the triangular geometry was proposed.The neutron flux distributions within a node were expanded in a series of analytic basis functions for each group.Nodes were coupled each other with both the zero-and first-order partial neutron current moments simultaneously.With a new sweeping scheme developed for triangular geometry,the response matrix technique was used to solve the nodal diffusion equations iteratively.Based on the proposed model,the code ABFEM-T was developed.The numerical results for a series of benchmark problems show that the core multiplication factor and nodal powers are predicted accurately using this model for unstructured neutron diffusion problems.